def test_matrix_to_coeff_conversion(self):
im = Immersion(50,50)
U = np.random.rand(*im.mat_shape)
Uc = im.matrix_to_coeffs(U)
U2 = im.coeffs_to_matrix(Uc)
for n in xrange(50):
npt.assert_allclose(np.sum(U[:,n]), np.sum(Uc[n].vector().array()),
rtol=1e-10, atol=1e-12)
npt.assert_allclose(U, U2, rtol=1e-10, atol=1e-12)
def test_derivative(self):
N = 100
M = 10
im = Immersion(M,N)
u = dol.Expression(('cos(x[0])/10.0','cos(x[0])/10.0'))
#u = dol.Expression(('0.1','0.1'))
u = dol.interpolate(u, im.V)
U = np.zeros(im.mat_shape)
u_scaler = 0.0
for n in xrange(im.N):
U[:,n] = u_scaler * u.vector().array()
S = im.calc_S(U)
dSarr = np.reshape(im.calc_dS(U),im.mat_shape)
vdS = 0
v = dol.Expression(('cos(x[0])/2.0','cos(x[0])/2.0'))
#v = dol.Expression(('pow(x[0],2)/3.0','pow(x[0],2)/3.0'))
#v = dol.Expression(('x[0]','x[0]'))
#v = dol.Expression(('x[0]*0.001','x[0]*0.001'))
v = dol.interpolate(v, im.V)
s_vdS = 0
s_v = 0
for dS in im.matrix_to_coeffs(dSarr):
#print "--->", dS.vector().array(), v.vector().array()
#print "--> ", np.sum(dS.vector().array()), np.sum(v.vector().array())
vdS += dol.assemble(dol.inner(v,dS)*dol.dx)
#print s_vdS * im.dt
vdS *= im.dt
lims = []
Ss = []
Sps = []
eps = 10.**(-sp.arange(20))
for ep in eps:
im = Immersion(M,N)
Up = np.zeros(im.mat_shape)
for n in xrange(im.N):
Up[:,n] = u_scaler * u.vector().array() + ep*v.vector().array()
Sp = im.calc_S(Up)
Ss.append(S)
Sps.append(Sp)
lims.append((Sp - S)/ep)
print "%s %15s %12s %12s %15s %15s" % ("Eps","LHS","RHS","S","Sp", "Sp - S")
for n in xrange(len(eps)):
print "%.0e %15.6f %12.6f %12.7f %12.7f %12.7f" % \
(eps[n], vdS, lims[n], Ss[n], Sps[n], Sps[n] - Ss[n])